Mass flow measurement of granular materials in aerial application. 1. Simulation and modeling

The mass flow of granular particles in an aerial spreader duct was regarded as a sequence of cluster passage events. At low flow densities, the total mass per time unit could be estimated by measuring the diameter (length) of each individual particle passing a sensor and accumulating the associated masses. At higher flow densities, the lengths of clusters would be measured rather than the lengths of particles. However, because of overlapping, the cluster lengths cannot simply be accumulated. The total length of a cluster is always smaller than the lengths of the individual particles within it. Therefore, a reconstruction method is necessary to estimate the total length of the particles within a cluster from the measured cluster length. This reconstruction algorithm was developed using MatLab as a simulation tool and was called the "Exponential Estimator." Simulations were conducted for particles with 1) Identical diameters, 2) Uniformly distributed diameters, 3) Gaussian distributed diameters, and 4) Urea-distributed diameters. A simple universal relationship was discovered between the event ratio (the ratio between the original number of particles in an experiment and the number of measured clusters) and the flow density. This relationship was found to be independent of both the mean diameter of particles and the diameter distribution, which is of great importance when mass flows of fertilizer are involved. The flow density cannot be measured directly. However, another simple relationship was found between the flow density and the number of clusters in certain length categories, which can be measured on the fly. This relationship was found to be independent of the mean diameter of particles, but dependent on the diameter distribution. Combination of these two relationships led to the Exponential Estimator. It contains only a single material-specific constant for distributed-diameter particles. The simplicity and compactness of the discovered relationships indicate the possibility to derive the Exponential Estimator from theoretical principles. The simulation tool as developed here could be a valuable instrument for this purpose.